Yes sir, your accumulated bonuses do count towards before combat skill tests. Those bonuses count towards everything unless otherwise specified and unless I am sorely mistaken vanilla Runebound has no such exceptions.
Always look carefully at the wording of cards though because some items only apply to combat situations, I've had friends try to get away with adding the Lightning Mace to a swim test, if they'd had the strength belt (actual name escapes me at the moment) they could because that provides a broad bonus to your body attribute, as if you had additional experience tokens, however, the mace applies only to combat rolls.
Thanks David - I figured equipment was by the wording of the card, just wasn't sure of the bonuses during before combat test.
Basically depending on the particular stat plus accumulated bonuses there could be before combat test where the Hero could have a high enough total as to not even take the test because he can't fail (this would seem to be the case even in some combat situations).
I wonder if there is a house rule where double ones always fail, just to add that extra layer of tension